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<Paper uid="C86-1045">
  <Title>Categorial Unification Grammars*</Title>
  <Section position="4" start_page="191" end_page="193" type="metho">
    <SectionTitle>
2. Motivation and Theoretical implications
</SectionTitle>
    <Paragraph position="0"> Both terms, unification grammar and categorial grammar are used for classes of grammar formalisms, for individual grammar formalisms, and finally for grammars that are written in these formalisms. In addition, they might also be used by linguists to denote linguistic theories that are built around or on top of such a formalism. This is the type of terminological overloading that linguists have learned to live with--or at least gotten accustomed to.</Paragraph>
    <Paragraph position="1"> As I indicated in the previous section, I consider CUG to stand for a family of grammar formalisms that might be described as the intersection of categorial and  unification grammar formalisms. What has been proposed so far is therefore not a new grammar formalism and even less a linguistic framework.</Paragraph>
    <Paragraph position="2"> The proposal is simply to further explore the usefulness and formal properties of subclasses of CUG. This proposal can be supported by a number of reasons. Both types of formalisms have clear advantages.</Paragraph>
    <Paragraph position="3"> Categorial grammars have been hailed for their conceptual clarity and their potentials for linking syntax and semantics. The fact that they have been around for a long time and that they are currently enjoying a renaissance in the works of Steedman, Bach, Dowty, and many others demonstrates their virtues. Unification grammars are spreading last and lend themselves to powerfifl but efficient computer implementations.</Paragraph>
    <Paragraph position="4"> Traditionally, categorial grammars have been lacking syntactic sophistication. In a functor category such as A/B, only domain and range of the function are specified but nothing is said about bow they are related; how, for instance, the features of the argument influence the features of the value. The graph notation expresses the relation between argument and value categories quite well; it is expressed in a set of bindings between subgraphs of the two categories.</Paragraph>
    <Paragraph position="5"> In the context of this discussion, some remarks are in order on the specific role PATR has played for the experiments with CUGs. The philosophy behind the development of PATR has been to provide a tool for writing, testing, and comparing grammars of very different types in a powerful formalism with well-understood formal properties and a well-defined semantics (Shieber 1984).</Paragraph>
    <Paragraph position="6"> Thus PATR could be useful for writing grammars, designing grammar formalisms, and for exploring classes of such formalisms. The work on exploring categorial unification formalisms has not only benefitted from the features of PATR but it has in a way also influenced the development of the PATR formalism. It was, for instance, essential for the writing of categorial grammars to allow category variables in the context-free phrase structure part of the rules. How else could one formulate the rules of functional application. The implementation of this facility through Stuart Shieber, however, raised interesting problems in connection with the prediction aspect of the Earley-parser. Original Earley prediction works on category symbols. An answer to these problems was presented by Shieber (1985) who proposed to do Earley prediction on the basis of some finite quotient of all constituent DAGs which can be specified by the grammar writer.</Paragraph>
    <Paragraph position="7"> Another example for the influence of the CUG efforts on the development of PATR is a new template notation introduced by Lauri Karttunen in his Interlisp-D version of PATR. Since categorial grammars exhibit an extensive embedding of categories within other categories, it is useful to unify templates not only with the whole lexical DAG but also with its categorial subgraphs. The @-notation permits this use of templates (Karttunen, 1986)3  3. A CUG Grammar Model that Aecomodates Word</Paragraph>
    <Section position="1" start_page="192" end_page="193" type="sub_section">
      <SectionTitle>
Order Variation
</SectionTitle>
      <Paragraph position="0"> Worder order variation has always been one of the hardest problems for categorial grammars. Functional composition together with type-raising can be used to obtain all permutations of the sentences that are generated by a traditional categorial grammar. Totally free word order does therefore not pose an unsurmountable problem to the categorial approach. As with other types of grammar formalisms, it is semi-free word order that is difficult to accommedate.</Paragraph>
      <Paragraph position="1"> GPSG, LFG, and FUG all have mechanisms for encoding ordering regularities. Such a device does not exist in the categorial grammars that i am aware of.</Paragraph>
      <Paragraph position="2"> However, Uszkoreit (1985a,b) argues (on the basis of data fl'om German) for an application of l/near precedence rules to the valency list of syntactic functors. This approach presupposes that the valency list contains adjuncts as well as complements as the flmetor's syntactic arguments) The model can be summarized as follows. The lexicon lists uninstantiated entries. For functors, these entries contain a set of thematic roles. The uninstantiated lexical entry may also state whether thematic roles have to be filled, whether they may be filled more than once, and whether idiosyncratic properties of the fnnetor predetermine the syntactic features of certain syntactic arguments.</Paragraph>
      <Paragraph position="3"> There are three types of rules that instantiate lexical entries: feature instantiation rules, valency instantiation rules, and order instantiation rules.</Paragraph>
      <Paragraph position="4"> An instantiated functor has an ordered valency list containing syntactic specifications of complements and adjuncts together with the appropriate semantic bindings. The model can account for the interspersing of complements and adjuncts as they occur in many languages including English. The model can also account for right-extraposition phenomena.</Paragraph>
      <Paragraph position="5"> t Therefore, the valency list may constain adjuncts that do not fill a thematic role of the functor but combine semantically with some constituent inside a linearily preceding member of the same valency listfi In the proposed model, the dependency between the extraposed phrase and its antecendent is neither established by functional application/composition nor by feature passing. It is assumed that there is a different matching process that combines the noncontiguous phrases. A process of this kind is independently needed for the matching of adjuncts with thematic roles that are embedded in the meaning of the functor: (26a) Tellme about French history.</Paragraph>
      <Paragraph position="6"> (26b) Start in 1700.</Paragraph>
      <Paragraph position="7"> The year 1700 is obviously not the start time for the telling.</Paragraph>
      <Paragraph position="8"> (27a) His call was very urgent.</Paragraph>
      <Paragraph position="9"> (27b) lie tried desperately from every phone booth on campus.</Paragraph>
      <Paragraph position="10"> It is not try that supplies here the source role but the implicit theme of try. If the theme role is filled, everybody would analyze the from PP as semantically belonging to the theme of try: (28) He tried to call her desperately from every phone booth on campus.</Paragraph>
      <Paragraph position="11"> I want to conclude this discussion with a remark on the parsing problem connected with the proposed model. In older PATR Phrase-Structure grammars as well as in the categorial PATR grammars, all graphs that may be connected with a word in the input string are either retrieved from the lexicon or from a cache of ah'eady built lexical graphs, or they are constructed on the spot fi'om the \[exical entries through the morphology and through lexical rules.</Paragraph>
      <Paragraph position="12"> For obvious reasons, this approach cannot be used in conjunction with the categorial model just proposed. If all adjuncts are included in the valency list, and if moreover all acceptable linearizations are performed in the extended lexicon, there is no upper bound on the number of acceptable lexieal graphs for functors. This means that lexical entries cannot be fully instantiated when the word is recognized. \]'hey need to be instantiated incrementally as potential arguments are encountered.</Paragraph>
      <Paragraph position="13"> In Uszkoreit (1985b) it is argued that the ordered valency lists of a functor admitted by the lexical \[nstantiation rules form a regular language. \[f further research confirms this hypothesis, the incremental {nstantiation of valency lists could be performed through sets of finite state machines.</Paragraph>
    </Section>
  </Section>
  <Section position="5" start_page="193" end_page="194" type="metho">
    <SectionTitle>
4. A Note on Long-distance Dependencies in CUGs
</SectionTitle>
    <Paragraph position="0"> In Steedman's (1985) categorial grammars, long-distance dependencies are endcoded in the function-argument structure of categories, The categories that form the path between filler and gap in a derivation tree all carry a valency slot for the filler. This uniform encoding of both subeategorization and long-distance dependencies in the argument structure of categories seems at first glance superior to the HPSG or PATR approaches to long-distance dependencies, in which the two types of information are marked in different feature sets. However, it turns out that the Steedman grammars have to mark the long-distance valency slots in order to distinguish them from other valency slots.</Paragraph>
    <Paragraph position="1"> There could still be a justification for encoding the two types of dependencies in the same argument stack.</Paragraph>
    <Paragraph position="2"> One might loose important nesting information by separating the two types of slots. However, I have not yet seen a convincing example of nesting constraints among subcategorization and long-distance dependencies.</Paragraph>
    <Paragraph position="3"> Therefore, I consider the question of the appropriate place for encoding long-distance dependencies still open. A last remark on long-distance dependencies. In a unification based system like PATR it is not trivial to ensure that gap information is passed up from one daughter constituent only when a rule is applied. There are two ways to enforce this constraint. The first one involves a multiplication of rules. For a binary rule A --&gt; B C, for instance, one could introduce three new rules, one of which does not do any gaP passing, another one the passing of a gap from B to A, and the third the passing of a gap from C to A.</Paragraph>
    <Paragraph position="4"> PATR uses a little more elegant method which has been first suggested by Fernando Pereira. Two features are threaded through every tree, one of which carries a gap up a tree, passing through all the constituents to the left of the gap, and a second one that is set to NIL if a gap has been found and that is then sent through all the constituents to the right of the gap, unifying it on the way with potential gaps. It requires that information about the two special features be added to every rule. In PATR a preprocessor of rules adds this information for all rules in which the grammar writer did not include any gap threading information herself, e.g., for encoding island constraints.</Paragraph>
    <Paragraph position="5"> In a CUG that only contains two (or at least very * few) rules, the first method of duplicating rules appears preferrable over the gap threading approach. Rules that propagate gap information might also include rules that permit parasitic gaps along the lines of Steedman's rules of functional substitution.</Paragraph>
    <Section position="1" start_page="194" end_page="194" type="sub_section">
      <SectionTitle>
Notes
</SectionTitle>
      <Paragraph position="0"> *The research for this paper was made possible through a gift by the System l)evelopment Foundation.</Paragraph>
      <Paragraph position="1"> tFor an introduction to the family of unification grammar models refer to Shieber (forthcmning). A good introduction to the basic notions ofcategorial grammar is Bar \[tiliel (1964).</Paragraph>
      <Paragraph position="2"> 2The PATti implementations that arc currently used at SR\[ actually permit cyc l ic graphs.</Paragraph>
      <Paragraph position="3"> :IRight-Node-Raising (RNR) which leads to sentences as: Peter likes and Paul buys bananas will be neglected here (although RNR is an attractive lopic for catcgorial grammarians and one of my grammars ~ctnally handles many cases of RNR.) IAn even lilt)re general notation can })e used that does not distinguish between root templates and subgraph templates. As long as template names are marked by some typographic convention.</Paragraph>
      <Paragraph position="4"> could be freely used wherever a graph is described.</Paragraph>
      <Paragraph position="5"> ~The version of t!le linear precedence rule component proposed b~ Uszkoreit {1982. 1986) is {\tlI&gt; compatible with this approach. The., proposal permit&gt; the formalization of partially free word order as \[t results fl'om the interaction of potentially conflicting ordering principles and as it probably occurs to some degree in all natural languages 6Sag (1985) proposes a mechanism for IIPSG that allows the syntactic binding of an extraposcd phrase to a complement or adjunct slot of a complement or adjunct. However, this approach is too restricted. Although there is a strong tendency to only extrapose complements and adiunets of top-level complements and adjuncts, there is certainly no such constraint in languages like English or German. The following sentence could not be handled since the extraposed relative clause modifies an adjunct of the subject.</Paragraph>
      <Paragraph position="6"> Petitions from those people were considered who had not filed a complaint before.</Paragraph>
      <Paragraph position="7"> 7Mark Johnson (1986) has worked out a quasi-categorial solution of this phenomenon in the framework of HPSG.</Paragraph>
    </Section>
  </Section>
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